Math Problem Statement

Let U = {1, 2, 3, 4, 5, 6, 7, 8}, A = {4, 6, 8}, B = {3, 4, 7, 10}, and C = {1, 3, 7}. Find the following. (Enter your answers as a comma-separated list.) A ∪ B

Solution

To find ABA \cup B, we need to take the union of sets AA and BB. The union of two sets contains all elements that are in either set, without duplication.

Given:

  • A={4,6,8}A = \{4, 6, 8\}
  • B={3,4,7,10}B = \{3, 4, 7, 10\}

The union ABA \cup B is the set of all elements that appear in either AA or BB:

AB={3,4,6,7,8,10}A \cup B = \{3, 4, 6, 7, 8, 10\}

Therefore, the answer is: 3,4,6,7,8,103, 4, 6, 7, 8, 10

Would you like more details on the steps? Also, here are 5 related questions to expand on this:

  1. What is the intersection of sets AA and BB?
  2. What is the complement of AA with respect to UU?
  3. How do you find ACA \cap C?
  4. What is (AB)C(A \cup B) \cap C?
  5. How would the union change if B={3,4,7}B = \{3, 4, 7\} instead of {3,4,7,10}\{3, 4, 7, 10\}?

Tip: In set theory, the union operation combines all unique elements from two sets.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Union of Sets

Formulas

A ∪ B = {x : x ∈ A or x ∈ B}

Theorems

Union of Sets

Suitable Grade Level

Grades 6-8